Asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipation

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• 作者：Masakazu Yamamoto^a ; ^{mk-yamamoto@ie.niigata-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Yuusuke Sugiyama^b ; ^{sugiyama@ma.kagu.tus.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B33 ; 35C20 ; 35K58 ; 35R11 ; 78A35 ; 82D37
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：141
• 期：Complete
• 页码：57-87
• 全文大小：739 K

文摘

The initial-value problem for the drift–diffusion equation arising from the model of semiconductor device simulations is studied. The dissipation on this equation is given by the fractional Laplacian (−Δ)^θ/2${(-\Delta )}^{\theta /2}$. Large-time behavior of solutions to the drift–diffusion equation with 0<θ≤1$0<\theta \le 1$ is discussed. When θ>1$\theta >1$, large-time behavior of solutions is known. However, when 0<θ≤1$0<\theta \le 1$, the perturbation methods used in the preceding works would not work. In this paper, the asymptotic expansion of solutions with high-order is derived.